Iran strikes back at American air base

IRAN has taken responsibility for a series of rockets that were fired at an Iraqi base hosting American soldiers.

Iranian state TV says Tehran launched "tens" of surface-to-surface missiles at Iraq's Ain Assad and Irbil air bases housing US troops at 1.30am local time (8.30am AEST).

Iranian officials said the attacks marked the beginning of a promised retaliation against the US for the killing of top Iranian military commander Qassem Soleimani.

"The fierce revenge by the Revolutionary Guards has begun," Iran's Islamic Revolutionary Guard Corps said in a statement on a Telegram channel.

It warned the US and its regional allies against retaliating over the missile attack: "We are warning all American allies, who gave their bases to its terrorist army, that any territory that is the starting point of aggressive acts against Iran will be targeted."

The attacks are significant as they mark the first direct retaliation against the US for Soleimani's death, following three days of mourning.

The direct attacks on US troops add to growing fears of a war between the US and Iran.

State TV said the operation's name was "Marytr Soleimani", and that the Revolutionary Guard's aerospace division, which controls Iran's missile program, launched the attacks.

It was not immediately clear whether the purported missile strikes struck the base or whether any damage has been caused. There was no confirmation from the US or anti-ISIS coalition partners on whether an attack has occurred.

Ain Assad air base is located in Iraq's western Anbar province. It was first used by American forces after the 2003 US-led invasion that toppled dictator Saddam Hussein. It later saw American troops stationed there amid the fight against the Islamic State group in Iraq and Syria.

State TV said the operation's name was "Marytr Soleimani". It said the Revolutionary Guard's aerospace division, which controls Iran's missile program, launched the attack.

White House press secretary Stephanie Grisham said the White House was aware of the reports.

"The President has been briefed and is monitoring the situation closely and consulting with his national security team," she said.

Prime Minister Scott Morrison has been in contact with the chiefs of the Defence force and the Ministers for Defence and Foreign Affairs regarding the incident.

It comes two days after rockets were fired near the US Embassy in Baghdad in the wake of the assassination of Soleimani.

Two rockets hit near the US embassy in Baghdad on Sunday, marking the second night in a row that the Green Zone was hit and the 14th time over the past two months that US installations have been targeted.

A third rocket simultaneously hit a family home outside the Green Zone, wounding four.

Ties between Iraq and the US have deteriorated following Soleimani's death.

Some 5,200 US soldiers are stationed across Iraqi bases to support local troops preventing a resurgence of the Islamic State jihadist group.

They are deployed as part of the broader international coalition, invited by the Iraqi government in 2014 to help fight IS.